Which expression is equivalent to 7^4 * 2^4? Choices: (A)14^4 (B)14^8 (C)1/14^4 (D)14^16

Identify Bases and Exponents: Identify the bases and the exponents in the expression 7^4 * 2^4. We have two bases, 7 and 2, each raised to the exponent 4. Base 1: 7 Exponent 1: 4 Base 2: 2 Exponent 2: 4Apply Exponent Property: Apply the property of exponents for multiplication with the same exponent but different bases. When we multiply two powers with the same exponent but different bases, we can combine the bases and keep the exponent the same. 7^4 * 2^4 = (7 * 2)^4Calculate Base Product: Calculate the product of the bases. Multiply the bases 7 and 2. 7 * 2 = 14Write Combined Expression: Write the expression with the combined base and the same exponent. (7 * 2)^4 = 14^4Choose Equivalent Expression: Choose the equivalent expression for 7^4 * 2^4. From the calculations above, we can see that 7^4 * 2^4 is equivalent to 14^4.

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Math Problems

Grade 8

Identify equivalent expressions involving exponents I

Full solution

Q. Which expression is equivalent to

7^4 \times 2^4

\newline

Choices:

\newline

(A)

14^4

\newline

(B)

14^8

\newline

(C)

\frac{1}{14^4}

\newline

(D)

14^{16}

Identify Bases and Exponents: Identify the bases and the exponents in the expression $7^4 \times 2^4$ . We have two bases, $7$ and $2$ , each raised to the exponent $4$ . Base $1$ : $7$ Exponent $1$ : $4$ Base $2$ : $2$ Exponent $2$ : $4$
Apply Exponent Property: Apply the property of exponents for multiplication with the same exponent but different bases. $\newline$ When we multiply two powers with the same exponent but different bases, we can combine the bases and keep the exponent the same. $\newline$ $7^4 \times 2^4 = (7 \times 2)^4$
Calculate Base Product: Calculate the product of the bases. $\newline$ Multiply the bases $7$ and $2$ . $\newline$ $7 \times 2 = 14$
Write Combined Expression: Write the expression with the combined base and the same exponent. $\newline$ $(7 \times 2)^4 = 14^4$
Choose Equivalent Expression: Choose the equivalent expression for $7^4 \times 2^4$ . From the calculations above, we can see that $7^4 \times 2^4$ is equivalent to $14^4$ .